A measure $\pi$ satisfies the detailed balance condition if
$$ \pi_i P_{ij} = \pi_j P_{ji}, \quad \forall i,j. $$If $\pi$ satisfies the detailed balance condition, then $\pi$ is also a stationary measure.
For the $j$ th component, $$ \sum_i \pi_i P_{ij}
\sum_i \pi_j P_{ji}
\pi_j \sum_i P_{ji}
\pi_j. $$
So detailed balance provides a sufficient condition for stationarity.
Detailed balance is a useful tool for finding a stationary measure.
A Markov chain that satisfies the detailed balance condition is called reversible.